利用等差数列构造大围长准循环低密度奇偶校验码

Construction of Quasi-cyclic Low-density Parity-check Codes with a Large Girth Based on Arithmetic Progression

针对准循环低密度奇偶校验(QC-LDPC)码中准循环基矩阵的移位系数确定问题,该文提出基于等差数列(AP)的确定方法。该方法构造的校验矩阵的围长至少为8,移位系数由简单的数学表达式确定,节省了编解码存储空间。研究结果表明,该方法对码长和码率参数的设计具有较好的灵活性。同时表明在加性高斯白噪声(AWGN)信道和置信传播(BP)译码算法下,该方法构造的码字在码长为1008、误比特率为510-时,信噪比优于渐进边增长(PEG)码近0.3 d B。

To cope with the issue of determining cyclic shift coefficients of the quasi-cyclic sub-matrix in the Quasi-Cyclic Low-Density Parity-Check（QC-LDPC） codes, a method is presented based on the Arithmetic Progression（AP） to compute the cyclic shift coefficients. By this method, the girth of its Tanner graph is at least eight, and the cyclic shift coefficients can be expressed in simple analytic expressions to reduce required memory usage. The simulation results show that the proposed algorithm has high flexibility with respect to the design of code length and rate. Furthermore, over an Additive White Gauss Noise（AWGN） channel and under the Belief Propagation（BP） decoding algorithm, the simulation result also represents that the SNR of the proposed QC-LDPC codes is better than the Progressive Edge-Growth（PEG） codes close to 0.3 d B at the code length of 1008 and BER performance of 10^-5.